Demand and price elasticity
Price elasticity of demand measures how strongly quantity responds to price: elasticity = percentage change in quantity / percentage change in price. Demand is elastic if the absolute value is above 1, so a price cut raises revenue, and inelastic if below 1, so a price rise raises revenue.
| Elasticity (absolute) | Type | Revenue effect of a price rise |
|---|---|---|
| Above 1 | Elastic | Revenue falls |
| Equal to 1 | Unit elastic | Revenue unchanged |
| Below 1 | Inelastic | Revenue rises |
Elasticity depends on substitutes, necessity, the share of budget, time to adjust and how narrowly the market is defined. Business customers locked into a supplier tend to be less price sensitive than consumers choosing among shelf brands.
The profit-maximizing price
A firm maximizes profit by producing where marginal revenue equals marginal cost (MR = MC). With a straight-line demand curve, you can solve it directly.
Profit maximization (hypothetical)
Demand: Q = 1,000 - 20P, so price as a function of quantity is P = 50 - Q/20. Unit cost is constant at $10, so MC = 10.
Revenue = P x Q = 50Q - Q squared / 20. Marginal revenue = 50 - Q/10. Set MR = MC: 50 - Q/10 = 10, so Q/10 = 40 and Q = 400. Then P = 50 - 400/20 = $30.
Profit = (30 - 10) x 400 = $8,000.
| Price | Quantity (1,000 - 20P) | Margin per unit | Profit |
|---|---|---|---|
| $25 | 500 | $15 | $7,500 |
| $30 | 400 | $20 | $8,000 |
| $35 | 300 | $25 | $7,500 |
The table confirms $30 is best: profit is lower at $25 and $35. Notice how profit falls on both sides because a higher margin on fewer units and a lower margin on more units trade off.
Elasticity and the markup rule
At the profit-maximizing price, there is a neat link between margin and elasticity (the Lerner rule): (P - MC) / P = 1 / |elasticity|.
In the example, elasticity at P = 30 and Q = 400 is -20 x 30 / 400 = -1.5. Then 1 / 1.5 = 0.667 and (30 - 10) / 30 = 0.667. The rule holds.
| Elasticity (absolute) | Optimal margin on price | Optimal markup on cost |
|---|---|---|
| 1.5 | 66.7 percent | 200 percent |
| 2 | 50 percent | 100 percent |
| 4 | 25 percent | 33 percent |
The implication for strategy is powerful: charge more where customers are less price sensitive and less where they are more sensitive, which leads to price discrimination, provided you can separate the groups and prevent resale.
Price discrimination and versioning
Charging different prices to different customers captures more surplus. It needs three conditions: market power, a way to separate customers and no easy resale.
| Type | How it works | Example |
|---|---|---|
| First degree | Each customer pays their maximum | Negotiated enterprise contracts |
| Second degree | Customers self-select through versions or quantity | Economy and business class; volume discounts |
| Third degree | Different prices for identifiable groups | Student and senior discounts; regional prices |
For an assignment, test fairness and legality as well as profit. Differences in price must rest on defensible grounds, and perceived unfairness can hurt the brand.
Strategic pricing: the price war game
When a few firms compete, each firm's best price depends on the others. Game theory models it. Consider two firms choosing High or Low price, with profits in $ millions (Firm A, Firm B).
| B: High | B: Low | |
|---|---|---|
| A: High | 10, 10 | 4, 14 |
| A: Low | 14, 4 | 6, 6 |
If B prices High, A earns 14 by pricing Low versus 10 by pricing High. If B prices Low, A earns 6 by pricing Low versus 4 by pricing High. So Low is A's best response whatever B does, and the same holds for B. The outcome is (Low, Low) with 6 each, even though both would prefer (High, High) with 10 each. This is the prisoner's dilemma, and it explains why price wars happen and why firms try to avoid them by competing on features, building loyalty or signaling commitment.
In repeated play, firms can sustain high prices if the future matters enough: cutting price gains 4 once but risks a lasting price war that costs 4 per period. Real markets also change the picture through differentiation, capacity and the threat of new entrants. See our strategic management guide for the industry view.
Working on this assignment now? Get a price for help with your paper.
Get an instant quoteCalculating elasticity from data
With two observed points rather than a demand equation, use the midpoint (arc) method so that the answer does not depend on direction.
Arc elasticity (hypothetical)
A price rise from $10 to $12 cuts weekly quantity from 500 to 430 units.
Percentage change in quantity = (430 - 500) / ((430 + 500) / 2) = -70 / 465 = -15.05 percent. Percentage change in price = (12 - 10) / ((12 + 10) / 2) = 2 / 11 = 18.18 percent.
Elasticity = -15.05 / 18.18 = -0.83, inelastic. Revenue rose from 10 x 500 = $5,000 to 12 x 430 = $5,160, consistent with inelastic demand.
Whether profit rose depends on cost. If unit cost is $6, profit went from 4 x 500 = $2,000 to 6 x 430 = $2,580. Note, though, that the price that maximizes revenue is not the one that maximizes profit when costs are positive, so always compare profit, not just revenue.
Bundling: why a package can beat separate prices
Bundling works when customers disagree about the value of individual items but their values for the whole package are similar. Suppose two customers value software and support differently, and marginal cost is zero.
| Customer | Value of software | Value of support | Value of both |
|---|---|---|---|
| A | $100 | $40 | $140 |
| B | $60 | $80 | $140 |
Separate prices: software at $60 sells to both (120) or at $100 to A only (100), so the best is $120. Support at $40 sells to both (80) or at $80 to B only (80), so the best is $80. Total = $200.
Bundle at $140: both customers value the bundle at $140 and buy it: total = $280.
The bundle earns $80 more, because it smooths out the differences in valuation. Discuss limits: it works less well when valuations are positively correlated, when costs differ among items or when customers can buy the parts elsewhere.
Writing a pricing recommendation
| Step | What to show |
|---|---|
| Customers and value | Who buys, what it is worth to them and how sensitive they are |
| Costs | Variable and fixed cost, and the break-even volume at the proposed price |
| Competition | Rivals' prices and likely responses |
| Price and structure | Level, tiers, discounts, bundles, with reasons |
| Numbers | Profit at two or three prices; the effect of a plausible demand error |
| Risks and monitoring | Signals to change price and how often to review |
Writing the analysis
- Estimate demand with evidence Use data, tests or comparable markets, and state uncertainty.
- Show marginal analysis Marginal revenue against marginal cost, not average cost.
- Link price to elasticity Explain why the margin is what it is.
- Consider rivals Expected reactions, and whether price is a good weapon.
- Add non-price factors Brand, positioning and customer relationships.
For the customer side, see our marketing management guide. If you want help with a pricing or managerial economics assignment, you can order MBA assignment help.